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#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
const int N=5e4+5;
const int ts=5e6;
const int A=70;
const int iu=64;
bool debug=false;

int n,m;
int a[N];
int ans[N];

int f[ts],lc[ts],rc[ts];
int sz=0;
vector<int>avail;
void print_tree(int id,int l,int r){
	if(id==0) return;
	cout << "tree " << id << ' ' << f[id] <<  ' ' << l << ' ' << r << endl;
	if(l==r) return;
	int mid=(l+r)/2;
	print_tree(lc[id],l,mid);
	print_tree(rc[id],mid+1,r);
}
int get(){
	sz=avail.back();avail.pop_back();
	lc[sz]=rc[sz]=f[sz]=0;
	return sz;
}
void give(int id){
	if(id!=0)
		avail.push_back(id);
}
int find(int id,int l,int r,vector<int>&trees,int need){//largest position where 
	if(l==r) return l-1;
	int mid=(l+r)/2;
	int rsz=0;
	for(auto c:trees) rsz+=f[rc[c]];
	if(rsz<need){
		for(auto &c:trees) c=lc[c];
		return find(id*2,l,mid,trees,need-rsz);
	}
	else{
		for(auto &c:trees) c=rc[c];
		return find(id*2+1,mid+1,r,trees,need);
	}
}
int upd(int id,int l,int r,int p){
	if(id==0){
		id=get();
	}
	if(l==r){
		f[id]++;
		return id;
	}
	int mid=(l+r)/2;
	if(p<=mid) lc[id]=upd(lc[id],l,mid,p);
	else rc[id]=upd(rc[id],mid+1,r,p);
	f[id]=f[lc[id]]+f[rc[id]];
	return id;
}
pair<int,int>split(int id,int l,int r,int p){
	if(id==0) return {0,0};
	if(r<=p) return {id,0};
	if(p<l) return {0,id};
	int mid=(l+r)/2;
	if(p<=mid){
		auto tmp=split(lc[id],l,mid,p);
		int newi=(tmp.fi==0)?0:get();
		lc[newi]=tmp.fi,rc[newi]=0;
		f[newi]=f[lc[newi]]+f[rc[newi]];
		lc[id]=tmp.se;
		f[id]=f[lc[id]]+f[rc[id]];
		
		return {newi,id};
	}
	else{
		auto tmp=split(rc[id],mid+1,r,p);
		int newi=(tmp.se==0)?0:get();
		lc[newi]=0,rc[newi]=tmp.se;
		f[newi]=f[lc[newi]]+f[rc[newi]];
		rc[id]=tmp.fi;
		f[id]=f[lc[id]]+f[rc[id]];
		return {id,newi};
	}
}




int newi[A];//x will move if paid j gold
int oldi[A][A];//ax = i and at old king's rule, x was paid j gold
vector<int>factor[A];

void kill_newi(int id,int l,int r){///move all tree elems to oldi
	if(id==0) return;
	////cout << "kill_newi " << id << ' ' << l << ' ' << r << endl;
	if(l==r){//move to oldi[a[i]][0]
		//cout << "killed newi " << r << endl;
		oldi[a[r]][0]=upd(oldi[a[r]][0],1,n,r);
		
	}
	else{
		int mid=(l+r)/2;
		kill_newi(lc[id],l,mid);
		kill_newi(rc[id],mid+1,r);
	}
	give(id);
}
void sav_newi(int id,int l,int r,int v){//move all tree elems to 
	if(id==0) return;
	if(l==r){//move to oldi[a[i]][0]
		int loc=min(iu+1,v+a[r]);
		ans[r]=v;
		newi[loc]=upd(newi[loc],1,n,r);
		
	}
	else{
		int mid=(l+r)/2;
		sav_newi(lc[id],l,mid,v);
		sav_newi(rc[id],mid+1,r,v);
	}
	give(id);
}
void save_newi(int &id,int l,int r,int v){
	sav_newi(id,l,r,v);
	id=0;
}
int merge(int id1,int id2,int l,int r){
	if(id1==0 || id2==0) return id1+id2;
	int mid=(l+r)/2;
	lc[id1]=merge(lc[id1],lc[id2],l,mid);
	rc[id1]=merge(rc[id1],rc[id2],mid+1,r);
	give(id2);
	f[id1]=f[lc[id1]]+f[rc[id1]];
	return id1;
}
void kill_oldi(int id,int l,int r,int &v){
	if(!id) return;
	//cout << "KILL OLD " << ' ' << oldi[1][0] << ' ' << v << endl;
	//print_tree(id,1,n);
	v=merge(v,id,1,n);
}
void set_ans(int id,int l,int r,int tar){
	if(id==0) return;
	if(l==r){
		ans[l]=tar-a[l];
		return;
	}
	int mid=(l+r)/2;
	set_ans(lc[id],l,mid,tar);
	set_ans(rc[id],mid+1,r,tar);
}
int main(){
	ios::sync_with_stdio(false);cin.tie(0);
	for(int i=1; i<=iu ;i++){
		for(int j=i; j<=iu ;j+=i) factor[j].push_back(i);
	}
	avail.resize(ts-1);
	for(int i=0; i<avail.size() ;i++) avail[i]=i+1;
	reverse(avail.begin(),avail.end());
	cin >> n >> m;
	for(int i=1; i<=n ;i++){
		cin >> a[i];
	}
	int king=n+1;
	for(int i=n; i>=1 ;i--){
		if(debug) cout << "Doing " << i << endl;
		
		int need=(n-i)/2 - (king-i-1);//
		int have=0;
		int cost=0;
		bool win=false;
		
		for(int j=0; j<=iu ;j++){
			int frog=f[newi[j]];
			for(auto c:factor[j]){
				frog+=f[oldi[c][j-c]];
			}
			if(have+frog<need){
				have+=frog;
				cost+=frog*j;
				continue;
			}
			if(cost+(need-have)*j>m) break;
			win=true;
			if(debug) cout << "Win " << j << ' ' << cost+(need-have)*j << endl;
			vector<int>fix;
			int thres;
			{//compute thres
				vector<int>v;
				if(newi[j]) v.push_back(newi[j]);
				for(auto c:factor[j]){
					if(oldi[c][j-c]) v.push_back(oldi[c][j-c]);
				}
				thres=find(1,1,n,v,need-have);///////////people asking for <j gold + people with id <=t and asking for j gold will be rewarded
				
			}
			if(debug) cout << "plan " << j << ' ' << thres << endl;
			{//process old
				for(int c=1; c<=iu ;c++){
					vector<int>kills;
					for(int k=(iu/c)*c; k>=0 ;k-=c){
						if(k+c>=j){
							if(k+c==j){
								auto tmp=split(oldi[c][k],1,n,thres);swap(tmp.fi,tmp.se);
								oldi[c][k+c]=tmp.fi;
								oldi[c][k]=tmp.se;
							}
							if(k!=0){
								kills.push_back(oldi[c][k]);
								oldi[c][k]=0;
							}
						}
						else{
							oldi[c][k+c]=oldi[c][k];
							oldi[c][k]=0;
						}
					}
					for(auto d:kills) kill_oldi(d,1,n,oldi[c][0]);
				}
			}
			if(debug) cout << "old done" << endl;
			{//process newi
				for(int k=iu+1; k>j ;k--){
					kill_newi(newi[k],1,n);
					newi[k]=0;
				}
				//print_tree(newi[j],1,n);
				auto tmp=split(newi[j],1,n,thres);swap(tmp.fi,tmp.se);
				kill_newi(tmp.se,1,n);
				if(debug) cout << "!!!!!!!!!! " << endl;
				if(debug) print_tree(tmp.fi,1,n);
				save_newi(tmp.fi,1,n,j);
				newi[j]=0;
				for(int k=j-1; k>=0 ;k--){
					save_newi(newi[k],1,n,k);
					newi[k]=0;
				}
			}
			if(debug) cout << "newi done" << endl;
			{//process dead
				for(int j=i+1; j<king ;j++){
					oldi[a[j]][0]=upd(oldi[a[j]][0],1,n,j);
				}
				king=i;
				ans[king]=m-(cost+(need-have)*j);
				int loc=min(iu+1,ans[king]+a[king]);
				if(debug) cout << "LOC " << loc << endl;
				newi[loc]=upd(newi[loc],1,n,king);
			}
			if(debug) cout << "dead done" << endl;
			break;
		}
		//print_tree(oldi[1][0],1,n);
		if(debug) cout << endl;
	}
	for(int i=1; i<king ;i++) ans[i]=-1;
	for(int c=1; c<=iu ;c++){
		for(int k=0; k<=iu ;k+=c){
			set_ans(oldi[c][k],1,n,k+c);
		}
	}
	for(int i=1; i<=n ;i++) cout << ans[i] << ' ';
	cout << '\n';
}